Tankless
2-cents' worth from the other side of the 'pond'.....
'Tankless' water heating sounds like what we know as 'Combination' boilers, which run the heating and provide 'instant' domestic hot water (DHW), but only at quite low flow-rates - sufficiently low that long pipe runs would certainly need to be well lagged (yes, even indoors!!) if you want a reasonable temperature at the tap/faucet. They are being fitted as standard equipment in nearly all new builds here, and as an 'upgrade' to anyone foolish enough to get taken in by the sales pitch. I wouldn't touch one if I was paid to!! If considering getting one of these, add the cost of a suitable standby generator into the cost. In the event of a power outage you not only have no heat or light, you also have no DHW. I know a few people living in 'all electric' houses and apartments who can't even heat some water on their stove (range) because it, too is electric.
Not sure what the situation is Statesside, but on this side of the 'pond', pretty much every batch of T.V. adverts includes at least one for 'boiler breakdown insurance', because people have been gullible enough to get 'talked into' one of these, and now live in constant fear of a breakdown. Needless to say, insurance companies and plumbers are laughing all the way to the bank (the insurers more so than the plumbers, I've worked on a couple of these, they are overcomplex, over-compacted, and generally not pleasant to work on. :-(
They may save some space in very small apartments, but that is their sole advantage / field of application IMHO. ;-)
Rant over
Dave T
P.S. A Eronie said (Reply#4) another disadvantage of this type of water heater is that there is a serious 'warm-up' delay which means that most (if not all) 'automatic' appliances effectively become 'cold fill only', because the pipework WILL have cooled down between fills, unless well lagged (insulated). :-(