Depends. As a general rule you would not want to get all the way to #1 holding short position while still on Ground Control. Something is already going wrong if you’re there.
Whether you solve that by switching to tower on your own or querying the ground controller for a handoff depends on how big the airport is. Small fields switching on your own is common. As a rule of thumb, once you’ve passed the last place where another airplane could appear at an intersection, it’s time to swap over.
At large airports you stick with ground until told to switch, or until you decide to ask GC for the handoff because you think you’ve been forgotten.
The bigger picture is that the sooner you’re listening to tower, the sooner you’ll begin to develop situational awareness of who’s taking off, who’s where on approach, what the wind is, etc. Since jets don’t do runups, our ideal is to arrive at the end of the runway as quickly as possible, and also to be cleared into position or for takeoff immediately. We’re not trying to hurry, in fact we’re actively trying not to hurry, but also trying to avoid any unnecessary delay by being fully ready to go internally, and also by already listening / talking to the right people before we get to the approach end of the runway.
Many large airports have multiple tower frequencies continuously in use. DFW has 4 tower freqs, although usually only 2 are used for takeoffs; sometimes 3 are used for takeoffs. They also have 3 GC freqs. ATL and ORD are similarly complex.
At MIA there are two tower freqs and if you haven’t been handed off to tower by about a half mile before the approach end of the runway it’s time to ask; There are 4 streams of airplanes on 4 taxiways leading to the crotch of 2 runways forming a V. GC puts each stream in order, but it’s tower that deals the next jet off one of the 4 streams onto one of the two runways. And sometimes swaps folks between streams on various cross taxiways. Tower can’t do their sorting and swapping unless they’re talking to everybody down at that end of the airport.
Etc. Times another 150 airports we serve just on my airplane from my base. Having familiarity with the local “house rules” is a valuable asset, one built up mostly by experience, plus some local “cheat sheet” type info distributed by the company.
At some airports there are signs along the parallel taxiway leading towards the runway saying “Change to tower 123.45 here”. Which may be a long ways short of the runway end, or right up close.
At some large airports it’s not always fixed which freq goes with which runway. So the only way to know which freq to switch to today when the winds are this way and they’re using Runways X and Y is for GC to tell you.
Relevant to this recent conversation about the JFK screw-up, JFK has two tower freqs used in different configurations depending on which way they’re aiming the airport. Sometimes GC does the handoff, or tells you something like “contact Tower 123.4 passing taxiway BW” which may at that time be a mile away and 20 minutes in your future. For at least one runway end they don’t do the handoff at all, they have “contact tower” signs set out about where you’d be #3 or 4 for departure given typical airliner sized jets.
Bottom line: the whole process is clear as mud and totally standardized and consistent. See? 
To be a little more fair, there is a consistent strategy to what’s going on. The tactics are all over the map based on local needs, but dealing with that is the difference between doing something for a living and doing something for a hobby. My brother builds houses. I go to Home Depot to buy stuff to make a mess out of fixing my house. He’s a pro and deals with complexities I’ve never heard of every day. Me, I just make a mess & draw blood. My blood.