if i have 3 routers connected and all have LANs behind them too.
i issue the >show ip route command and i see couple of routes that were learned via EIGRP and couple as Directly-Connected.
so when a host on the LAN sends a packet - will the router prefer the "Directly-Connected"(C) path?
i think that he will because the administrative distance is the smallest in directly connected routes, hence the most fast. am i right?
You are totally right, but i've tried to answer the simplest direct informative answer where the original poster can see the interaction between the EIGRP route and the connected route.
I'm sorry to put this question here but its a small one:
when i issue the >show ip route command
what does "* - candidate default" means?
suppose i have *S(static route), what does this mean?
Logically speaking the direct connected IPs should be those of the LAN directly connected to the router, and the EIGRP routes are those of the remote LANs behind the other 2 routers, if you post the output of the show ip route we can discuss it.
I cant its an image.
the serial cable between 2 of the 3 routers has an ip subnet above it(it is the serial interface of the second router) and it is shown as directly connected. and the question is if a message that originates from the LAN behind the first router goes to the LAN behind the second - what route will it choose?
To brief you out, each router should have the following entries in its routing table:
Its LAN as directly connected.
The other 2 LANs learned from EIGRP.
The WAN (serial) ips as directly connected.
Thus any packet destined to a serial ip, will use its directly connected route, and any packet destined to the remote LAN IP should use th EIGRP route.
 A packet going from the first LAN to another LAN, will use the EIGRP route and note that the EIGRP route's next-hop is the serial IP of the remote router, and thus the router will use the connected route of the serial interface to get the outgoing interface (recursive lookup).
Not wanting to confuse the issue but I believe that it is important to recognize that the router will use the EIGRP route - as you point out. And to recognize that the EIGRP route might not be over the connected serial interface. I can imagine a scenario where router1, router2, and router3 are connected forming a triangle. If the link between router1 and router3 is a very low speed high delay link, and if the links between router1 and router2 and the link between router2 and router3 are high speed low delay links, it is possible that the best EIGRP router from the LAN of router1 to the LAN of router3 will be on the serial link to router2.
may i ask a different question about EIGRP?:
what is FD?(Feasible Distance)
i know that RD is reported distance. so RD is the real distance and FD is an assumption(?)
The FD, is the lowest (best) calculated metric to a destination (successor), while the RD is the received distance from any downstream router, and accordingly the feasible condition states that for a route to be feasible FD>RD.