[old_tv_nut]

It depends on the particular situation. Some reasonably good analog transmitters could be converted to digital by substituting a digital exciter. The catch, however, is that stations usually needed to be on the air with both digital and analog during the transition (a few were allowed to do a direct cut), so new equipment had to be bought anyway. In some cases, equipment got cycled around as channel allocations were adjusted. Some stations went on the air in digital using a low power transmitter, then switched their more powerful analog transmitter to digital at the cutover, keeping the smaller digital transmitter as a backup. Or, the analog transmitter was switched to digital and diplexed with the other digital to get 3 dB more power.
In some cases, the analog transmitter was due for replacement in a few years, and the station just hung in there until they could turn it off and NOT replace it.

Edit: in the big cites where the stations lease space on tall buildings, there was a lengthy negotiation period with the stations playing building owners against each other before settling on the final location for the digital transmitters. In Chicago, it was of course Sears Tower vs. Hancock Building - but then there were also several stages of modifying the antenna farm on Sears.